For each of the following relations, determine whether the relation is: (i) Reflexive. (ii) Anti-reflexive. (iii) Symmetric. (iv) Anti-symmetric. (v) Transitive. (vi) A partial order. (vii) A strict order. (viii) An equivalence relation. Justify all your answers. You need to have eight answers for each question. a The domain of R is a group of students. Ry if x has earned more credits than y. (NOTE: You can assume there are at least two students who have not earned the same number of credits.) b R is a relation on Z such that Ry if and only if x - y = 3m for some integer m. c The domain R is the set of all cell phone towers in a network. Two towers can communicate if they are within a distance of three miles from each other. Ry if x can communicate with y. (NOTE: You can assume that there are at least two towers that are within three miles of each other.)

Give all the keys of R if the functional dependencies on R in each of the following cases

We studied different properties of relations like reflexive, symmetric, antisymmetric, transitive. Please provide one example relation each for each property of the relation. Try to come up with original examples which can be seen practically. (Example, Reflexive relation R = {(a, b) | a and b share same birthday},  Symmetric relation R = {(a, b) | a and b are friends}, Antisymmetric relation R = {(a, b) | a is instructor of b}, Transitive relation R = {(a, c) | a is sibling of b, b is sibling of c, then a is sibling of c}

Computer Science Match each of the following relations on S = {the set of all people in the US} with the correct category. Your answer should include all properties that apply to the relation. xρy ↔ x is the husband of y       [ Choose ]            Reflexive            Symmetric            Reflexive and Symmetric            Transitive            None            Symmetric and Transitive       xρy ↔ x has the same parents as y       [ Choose ]            Reflexive            Symmetric            Reflexive and Symmetric            Transitive            None            Symmetric and Transitive       xρy ↔ x is the spouse of y       [ Choose ]            Reflexive            Symmetric            Reflexive and Symmetric            Transitive            None            Symmetric and Transitive       xρy ↔ x is a brother of y       [ Choose ]            Reflexive            Symmetric            Reflexive and Symmetric            Transitive            None            Symmetric and Transitive

9.. Don't explain ... just tell me which is right... solve only if you are 100% sure

Consider the following five relations on the set A = {1, 2, 3, 4}. Determine which of the * .relations are reflexive R2 = {(1, 1)(1, 2), (2, 1), (2, 2), (3, 3), (4, 4)} R4 = A x A R1 = {(1, 1), (1, 2), (2, 3), (1, 3), (4, 4)} R3 = {(1, 3), (2, 1)}

whay decision can be achieved by a fuzzy relation?

2. Let N be a relation on R where Ny if and only if zy < 0. Is N reflexive? Is N symmetric? Is N transitive? Prove or provide a counterexample for each of these three properties.

let X = {0, 1}

Question 3 • Let A be the set A={a,b,c,d} and R is a relation on set A, where R = { (a,a), (a,b) ,(b,a),(b,b), (c,d),(c,c) ,(d,d)} Determine if R is a reflexive and symmetric relation on A.